Properties

Label 1110.2.l.a.43.1
Level $1110$
Weight $2$
Character 1110.43
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Character \(\chi\) \(=\) 1110.43
Dual form 1110.2.l.a.697.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.51129 - 1.64803i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.51129 - 1.64803i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(1.64803 - 1.51129i) q^{10} -0.350472i q^{11} +(0.707107 - 0.707107i) q^{12} +3.27075i q^{13} +(2.75974 + 2.75974i) q^{14} +(2.23398 + 0.0966903i) q^{15} +1.00000 q^{16} -7.07368 q^{17} +1.00000 q^{18} +(-2.01227 + 2.01227i) q^{19} +(1.51129 + 1.64803i) q^{20} +3.90286i q^{21} +0.350472 q^{22} -1.24836i q^{23} +(0.707107 + 0.707107i) q^{24} +(-0.432008 + 4.98130i) q^{25} -3.27075 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.75974 + 2.75974i) q^{28} +(-6.14644 - 6.14644i) q^{29} +(-0.0966903 + 2.23398i) q^{30} +(-2.76854 + 2.76854i) q^{31} +1.00000i q^{32} +(0.247821 + 0.247821i) q^{33} -7.07368i q^{34} +(-8.71889 - 0.377368i) q^{35} +1.00000i q^{36} +(-4.91116 + 3.58895i) q^{37} +(-2.01227 - 2.01227i) q^{38} +(-2.31277 - 2.31277i) q^{39} +(-1.64803 + 1.51129i) q^{40} +5.57830i q^{41} -3.90286 q^{42} +3.23195i q^{43} +0.350472i q^{44} +(-1.64803 + 1.51129i) q^{45} +1.24836 q^{46} +(5.76291 - 5.76291i) q^{47} +(-0.707107 + 0.707107i) q^{48} -8.23228i q^{49} +(-4.98130 - 0.432008i) q^{50} +(5.00185 - 5.00185i) q^{51} -3.27075i q^{52} +(-3.45760 - 3.45760i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-0.577588 + 0.529665i) q^{55} +(-2.75974 - 2.75974i) q^{56} -2.84578i q^{57} +(6.14644 - 6.14644i) q^{58} +(-10.6205 + 10.6205i) q^{59} +(-2.23398 - 0.0966903i) q^{60} +(1.30384 - 1.30384i) q^{61} +(-2.76854 - 2.76854i) q^{62} +(-2.75974 - 2.75974i) q^{63} -1.00000 q^{64} +(5.39030 - 4.94305i) q^{65} +(-0.247821 + 0.247821i) q^{66} +(-10.6169 - 10.6169i) q^{67} +7.07368 q^{68} +(0.882722 + 0.882722i) q^{69} +(0.377368 - 8.71889i) q^{70} +15.8980 q^{71} -1.00000 q^{72} +(-0.998067 + 0.998067i) q^{73} +(-3.58895 - 4.91116i) q^{74} +(-3.21684 - 3.82779i) q^{75} +(2.01227 - 2.01227i) q^{76} +(-0.967210 - 0.967210i) q^{77} +(2.31277 - 2.31277i) q^{78} +(-2.47200 + 2.47200i) q^{79} +(-1.51129 - 1.64803i) q^{80} -1.00000 q^{81} -5.57830 q^{82} +(-10.6094 - 10.6094i) q^{83} -3.90286i q^{84} +(10.6904 + 11.6576i) q^{85} -3.23195 q^{86} +8.69238 q^{87} -0.350472 q^{88} +(-3.03601 - 3.03601i) q^{89} +(-1.51129 - 1.64803i) q^{90} +(9.02641 + 9.02641i) q^{91} +1.24836i q^{92} -3.91530i q^{93} +(5.76291 + 5.76291i) q^{94} +(6.35741 + 0.275159i) q^{95} +(-0.707107 - 0.707107i) q^{96} +7.94277 q^{97} +8.23228 q^{98} -0.350472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{4} + 4q^{7} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{7} - 4q^{10} + 4q^{14} + 36q^{16} - 32q^{17} + 36q^{18} + 4q^{19} + 8q^{22} - 4q^{25} + 8q^{26} - 4q^{28} + 36q^{29} - 4q^{31} + 4q^{33} - 12q^{35} - 4q^{37} + 4q^{38} + 4q^{39} + 4q^{40} - 16q^{42} + 4q^{45} + 16q^{47} - 16q^{50} - 8q^{53} + 16q^{55} - 4q^{56} - 36q^{58} - 4q^{59} - 4q^{61} - 4q^{62} - 4q^{63} - 36q^{64} + 52q^{65} - 4q^{66} + 16q^{67} + 32q^{68} - 8q^{69} - 28q^{70} - 8q^{71} - 36q^{72} - 4q^{73} + 28q^{74} + 16q^{75} - 4q^{76} + 8q^{77} - 4q^{78} - 12q^{79} - 36q^{81} - 8q^{82} + 8q^{83} + 8q^{85} + 32q^{86} - 8q^{87} - 8q^{88} - 24q^{89} + 56q^{91} + 16q^{94} - 20q^{95} + 40q^{97} - 12q^{98} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −1.51129 1.64803i −0.675869 0.737022i
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) 2.75974 2.75974i 1.04308 1.04308i 0.0440528 0.999029i \(-0.485973\pi\)
0.999029 0.0440528i \(-0.0140270\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 1.64803 1.51129i 0.521153 0.477912i
\(11\) 0.350472i 0.105671i −0.998603 0.0528356i \(-0.983174\pi\)
0.998603 0.0528356i \(-0.0168259\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 3.27075i 0.907143i 0.891220 + 0.453572i \(0.149850\pi\)
−0.891220 + 0.453572i \(0.850150\pi\)
\(14\) 2.75974 + 2.75974i 0.737570 + 0.737570i
\(15\) 2.23398 + 0.0966903i 0.576810 + 0.0249653i
\(16\) 1.00000 0.250000
\(17\) −7.07368 −1.71562 −0.857810 0.513967i \(-0.828176\pi\)
−0.857810 + 0.513967i \(0.828176\pi\)
\(18\) 1.00000 0.235702
\(19\) −2.01227 + 2.01227i −0.461647 + 0.461647i −0.899195 0.437548i \(-0.855847\pi\)
0.437548 + 0.899195i \(0.355847\pi\)
\(20\) 1.51129 + 1.64803i 0.337935 + 0.368511i
\(21\) 3.90286i 0.851673i
\(22\) 0.350472 0.0747209
\(23\) 1.24836i 0.260301i −0.991494 0.130150i \(-0.958454\pi\)
0.991494 0.130150i \(-0.0415460\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) −0.432008 + 4.98130i −0.0864015 + 0.996260i
\(26\) −3.27075 −0.641447
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −2.75974 + 2.75974i −0.521541 + 0.521541i
\(29\) −6.14644 6.14644i −1.14137 1.14137i −0.988201 0.153165i \(-0.951053\pi\)
−0.153165 0.988201i \(-0.548947\pi\)
\(30\) −0.0966903 + 2.23398i −0.0176532 + 0.407866i
\(31\) −2.76854 + 2.76854i −0.497244 + 0.497244i −0.910579 0.413335i \(-0.864364\pi\)
0.413335 + 0.910579i \(0.364364\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.247821 + 0.247821i 0.0431401 + 0.0431401i
\(34\) 7.07368i 1.21313i
\(35\) −8.71889 0.377368i −1.47376 0.0637869i
\(36\) 1.00000i 0.166667i
\(37\) −4.91116 + 3.58895i −0.807389 + 0.590019i
\(38\) −2.01227 2.01227i −0.326433 0.326433i
\(39\) −2.31277 2.31277i −0.370340 0.370340i
\(40\) −1.64803 + 1.51129i −0.260576 + 0.238956i
\(41\) 5.57830i 0.871185i 0.900144 + 0.435592i \(0.143461\pi\)
−0.900144 + 0.435592i \(0.856539\pi\)
\(42\) −3.90286 −0.602224
\(43\) 3.23195i 0.492868i 0.969160 + 0.246434i \(0.0792588\pi\)
−0.969160 + 0.246434i \(0.920741\pi\)
\(44\) 0.350472i 0.0528356i
\(45\) −1.64803 + 1.51129i −0.245674 + 0.225290i
\(46\) 1.24836 0.184060
\(47\) 5.76291 5.76291i 0.840606 0.840606i −0.148331 0.988938i \(-0.547390\pi\)
0.988938 + 0.148331i \(0.0473902\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 8.23228i 1.17604i
\(50\) −4.98130 0.432008i −0.704462 0.0610951i
\(51\) 5.00185 5.00185i 0.700399 0.700399i
\(52\) 3.27075i 0.453572i
\(53\) −3.45760 3.45760i −0.474938 0.474938i 0.428571 0.903508i \(-0.359017\pi\)
−0.903508 + 0.428571i \(0.859017\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) −0.577588 + 0.529665i −0.0778820 + 0.0714200i
\(56\) −2.75974 2.75974i −0.368785 0.368785i
\(57\) 2.84578i 0.376933i
\(58\) 6.14644 6.14644i 0.807068 0.807068i
\(59\) −10.6205 + 10.6205i −1.38267 + 1.38267i −0.542832 + 0.839841i \(0.682648\pi\)
−0.839841 + 0.542832i \(0.817352\pi\)
\(60\) −2.23398 0.0966903i −0.288405 0.0124827i
\(61\) 1.30384 1.30384i 0.166940 0.166940i −0.618693 0.785633i \(-0.712338\pi\)
0.785633 + 0.618693i \(0.212338\pi\)
\(62\) −2.76854 2.76854i −0.351605 0.351605i
\(63\) −2.75974 2.75974i −0.347694 0.347694i
\(64\) −1.00000 −0.125000
\(65\) 5.39030 4.94305i 0.668584 0.613110i
\(66\) −0.247821 + 0.247821i −0.0305047 + 0.0305047i
\(67\) −10.6169 10.6169i −1.29707 1.29707i −0.930322 0.366744i \(-0.880473\pi\)
−0.366744 0.930322i \(-0.619527\pi\)
\(68\) 7.07368 0.857810
\(69\) 0.882722 + 0.882722i 0.106267 + 0.106267i
\(70\) 0.377368 8.71889i 0.0451041 1.04211i
\(71\) 15.8980 1.88675 0.943373 0.331733i \(-0.107633\pi\)
0.943373 + 0.331733i \(0.107633\pi\)
\(72\) −1.00000 −0.117851
\(73\) −0.998067 + 0.998067i −0.116815 + 0.116815i −0.763098 0.646283i \(-0.776323\pi\)
0.646283 + 0.763098i \(0.276323\pi\)
\(74\) −3.58895 4.91116i −0.417207 0.570910i
\(75\) −3.21684 3.82779i −0.371448 0.441995i
\(76\) 2.01227 2.01227i 0.230823 0.230823i
\(77\) −0.967210 0.967210i −0.110224 0.110224i
\(78\) 2.31277 2.31277i 0.261870 0.261870i
\(79\) −2.47200 + 2.47200i −0.278122 + 0.278122i −0.832359 0.554237i \(-0.813010\pi\)
0.554237 + 0.832359i \(0.313010\pi\)
\(80\) −1.51129 1.64803i −0.168967 0.184255i
\(81\) −1.00000 −0.111111
\(82\) −5.57830 −0.616020
\(83\) −10.6094 10.6094i −1.16454 1.16454i −0.983471 0.181065i \(-0.942046\pi\)
−0.181065 0.983471i \(-0.557954\pi\)
\(84\) 3.90286i 0.425836i
\(85\) 10.6904 + 11.6576i 1.15954 + 1.26445i
\(86\) −3.23195 −0.348510
\(87\) 8.69238 0.931921
\(88\) −0.350472 −0.0373604
\(89\) −3.03601 3.03601i −0.321816 0.321816i 0.527647 0.849464i \(-0.323074\pi\)
−0.849464 + 0.527647i \(0.823074\pi\)
\(90\) −1.51129 1.64803i −0.159304 0.173718i
\(91\) 9.02641 + 9.02641i 0.946225 + 0.946225i
\(92\) 1.24836i 0.130150i
\(93\) 3.91530i 0.405998i
\(94\) 5.76291 + 5.76291i 0.594398 + 0.594398i
\(95\) 6.35741 + 0.275159i 0.652256 + 0.0282308i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) 7.94277 0.806466 0.403233 0.915097i \(-0.367886\pi\)
0.403233 + 0.915097i \(0.367886\pi\)
\(98\) 8.23228 0.831586
\(99\) −0.350472 −0.0352238
\(100\) 0.432008 4.98130i 0.0432008 0.498130i
\(101\) 0.514124i 0.0511573i 0.999673 + 0.0255786i \(0.00814282\pi\)
−0.999673 + 0.0255786i \(0.991857\pi\)
\(102\) 5.00185 + 5.00185i 0.495257 + 0.495257i
\(103\) −9.07861 −0.894542 −0.447271 0.894398i \(-0.647604\pi\)
−0.447271 + 0.894398i \(0.647604\pi\)
\(104\) 3.27075 0.320724
\(105\) 6.43202 5.89834i 0.627701 0.575620i
\(106\) 3.45760 3.45760i 0.335832 0.335832i
\(107\) 1.33354 1.33354i 0.128919 0.128919i −0.639703 0.768622i \(-0.720943\pi\)
0.768622 + 0.639703i \(0.220943\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 2.30925 2.30925i 0.221186 0.221186i −0.587812 0.808998i \(-0.700010\pi\)
0.808998 + 0.587812i \(0.200010\pi\)
\(110\) −0.529665 0.577588i −0.0505015 0.0550709i
\(111\) 0.934944 6.01048i 0.0887410 0.570490i
\(112\) 2.75974 2.75974i 0.260770 0.260770i
\(113\) −7.85255 −0.738705 −0.369353 0.929289i \(-0.620421\pi\)
−0.369353 + 0.929289i \(0.620421\pi\)
\(114\) 2.84578 0.266532
\(115\) −2.05733 + 1.88663i −0.191847 + 0.175929i
\(116\) 6.14644 + 6.14644i 0.570683 + 0.570683i
\(117\) 3.27075 0.302381
\(118\) −10.6205 10.6205i −0.977698 0.977698i
\(119\) −19.5215 + 19.5215i −1.78953 + 1.78953i
\(120\) 0.0966903 2.23398i 0.00882658 0.203933i
\(121\) 10.8772 0.988834
\(122\) 1.30384 + 1.30384i 0.118044 + 0.118044i
\(123\) −3.94446 3.94446i −0.355660 0.355660i
\(124\) 2.76854 2.76854i 0.248622 0.248622i
\(125\) 8.86223 6.81623i 0.792662 0.609662i
\(126\) 2.75974 2.75974i 0.245857 0.245857i
\(127\) −14.6420 + 14.6420i −1.29927 + 1.29927i −0.370388 + 0.928877i \(0.620775\pi\)
−0.928877 + 0.370388i \(0.879225\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −2.28533 2.28533i −0.201212 0.201212i
\(130\) 4.94305 + 5.39030i 0.433534 + 0.472760i
\(131\) −3.62929 + 3.62929i −0.317093 + 0.317093i −0.847649 0.530557i \(-0.821983\pi\)
0.530557 + 0.847649i \(0.321983\pi\)
\(132\) −0.247821 0.247821i −0.0215701 0.0215701i
\(133\) 11.1067i 0.963070i
\(134\) 10.6169 10.6169i 0.917164 0.917164i
\(135\) 0.0966903 2.23398i 0.00832178 0.192270i
\(136\) 7.07368i 0.606563i
\(137\) −12.5315 + 12.5315i −1.07064 + 1.07064i −0.0733326 + 0.997308i \(0.523363\pi\)
−0.997308 + 0.0733326i \(0.976637\pi\)
\(138\) −0.882722 + 0.882722i −0.0751423 + 0.0751423i
\(139\) −3.66631 −0.310972 −0.155486 0.987838i \(-0.549694\pi\)
−0.155486 + 0.987838i \(0.549694\pi\)
\(140\) 8.71889 + 0.377368i 0.736880 + 0.0318934i
\(141\) 8.14998i 0.686352i
\(142\) 15.8980i 1.33413i
\(143\) 1.14631 0.0958590
\(144\) 1.00000i 0.0833333i
\(145\) −0.840469 + 19.4186i −0.0697972 + 1.61263i
\(146\) −0.998067 0.998067i −0.0826007 0.0826007i
\(147\) 5.82110 + 5.82110i 0.480116 + 0.480116i
\(148\) 4.91116 3.58895i 0.403695 0.295010i
\(149\) 16.9433i 1.38805i −0.719951 0.694025i \(-0.755836\pi\)
0.719951 0.694025i \(-0.244164\pi\)
\(150\) 3.82779 3.21684i 0.312538 0.262654i
\(151\) 10.7953i 0.878510i −0.898362 0.439255i \(-0.855242\pi\)
0.898362 0.439255i \(-0.144758\pi\)
\(152\) 2.01227 + 2.01227i 0.163217 + 0.163217i
\(153\) 7.07368i 0.571873i
\(154\) 0.967210 0.967210i 0.0779400 0.0779400i
\(155\) 8.74670 + 0.378572i 0.702552 + 0.0304076i
\(156\) 2.31277 + 2.31277i 0.185170 + 0.185170i
\(157\) 6.59408 6.59408i 0.526265 0.526265i −0.393192 0.919457i \(-0.628629\pi\)
0.919457 + 0.393192i \(0.128629\pi\)
\(158\) −2.47200 2.47200i −0.196662 0.196662i
\(159\) 4.88978 0.387785
\(160\) 1.64803 1.51129i 0.130288 0.119478i
\(161\) −3.44514 3.44514i −0.271515 0.271515i
\(162\) 1.00000i 0.0785674i
\(163\) −7.00131 −0.548385 −0.274193 0.961675i \(-0.588411\pi\)
−0.274193 + 0.961675i \(0.588411\pi\)
\(164\) 5.57830i 0.435592i
\(165\) 0.0338872 0.782946i 0.00263812 0.0609523i
\(166\) 10.6094 10.6094i 0.823451 0.823451i
\(167\) −14.7018 −1.13766 −0.568830 0.822455i \(-0.692604\pi\)
−0.568830 + 0.822455i \(0.692604\pi\)
\(168\) 3.90286 0.301112
\(169\) 2.30219 0.177091
\(170\) −11.6576 + 10.6904i −0.894101 + 0.819915i
\(171\) 2.01227 + 2.01227i 0.153882 + 0.153882i
\(172\) 3.23195i 0.246434i
\(173\) −3.00005 + 3.00005i −0.228090 + 0.228090i −0.811894 0.583805i \(-0.801563\pi\)
0.583805 + 0.811894i \(0.301563\pi\)
\(174\) 8.69238i 0.658968i
\(175\) 12.5548 + 14.9393i 0.949057 + 1.12931i
\(176\) 0.350472i 0.0264178i
\(177\) 15.0197i 1.12895i
\(178\) 3.03601 3.03601i 0.227559 0.227559i
\(179\) 9.62402 + 9.62402i 0.719333 + 0.719333i 0.968469 0.249136i \(-0.0801466\pi\)
−0.249136 + 0.968469i \(0.580147\pi\)
\(180\) 1.64803 1.51129i 0.122837 0.112645i
\(181\) 14.0878 1.04713 0.523567 0.851984i \(-0.324601\pi\)
0.523567 + 0.851984i \(0.324601\pi\)
\(182\) −9.02641 + 9.02641i −0.669082 + 0.669082i
\(183\) 1.84391i 0.136306i
\(184\) −1.24836 −0.0920302
\(185\) 13.3369 + 2.66980i 0.980546 + 0.196288i
\(186\) 3.91530 0.287084
\(187\) 2.47913i 0.181292i
\(188\) −5.76291 + 5.76291i −0.420303 + 0.420303i
\(189\) 3.90286 0.283891
\(190\) −0.275159 + 6.35741i −0.0199622 + 0.461215i
\(191\) 2.11691 + 2.11691i 0.153174 + 0.153174i 0.779534 0.626360i \(-0.215456\pi\)
−0.626360 + 0.779534i \(0.715456\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 20.7874i 1.49631i −0.663525 0.748154i \(-0.730940\pi\)
0.663525 0.748154i \(-0.269060\pi\)
\(194\) 7.94277i 0.570257i
\(195\) −0.316250 + 7.30678i −0.0226471 + 0.523249i
\(196\) 8.23228i 0.588020i
\(197\) −11.8547 + 11.8547i −0.844614 + 0.844614i −0.989455 0.144841i \(-0.953733\pi\)
0.144841 + 0.989455i \(0.453733\pi\)
\(198\) 0.350472i 0.0249070i
\(199\) 6.76638 + 6.76638i 0.479656 + 0.479656i 0.905022 0.425366i \(-0.139854\pi\)
−0.425366 + 0.905022i \(0.639854\pi\)
\(200\) 4.98130 + 0.432008i 0.352231 + 0.0305476i
\(201\) 15.0146 1.05905
\(202\) −0.514124 −0.0361737
\(203\) −33.9251 −2.38108
\(204\) −5.00185 + 5.00185i −0.350200 + 0.350200i
\(205\) 9.19321 8.43043i 0.642082 0.588807i
\(206\) 9.07861i 0.632537i
\(207\) −1.24836 −0.0867669
\(208\) 3.27075i 0.226786i
\(209\) 0.705244 + 0.705244i 0.0487828 + 0.0487828i
\(210\) 5.89834 + 6.43202i 0.407024 + 0.443852i
\(211\) −9.92928 −0.683560 −0.341780 0.939780i \(-0.611030\pi\)
−0.341780 + 0.939780i \(0.611030\pi\)
\(212\) 3.45760 + 3.45760i 0.237469 + 0.237469i
\(213\) −11.2416 + 11.2416i −0.770261 + 0.770261i
\(214\) 1.33354 + 1.33354i 0.0911592 + 0.0911592i
\(215\) 5.32635 4.88441i 0.363254 0.333114i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) 15.2809i 1.03733i
\(218\) 2.30925 + 2.30925i 0.156402 + 0.156402i
\(219\) 1.41148i 0.0953790i
\(220\) 0.577588 0.529665i 0.0389410 0.0357100i
\(221\) 23.1363i 1.55631i
\(222\) 6.01048 + 0.934944i 0.403397 + 0.0627494i
\(223\) −6.49659 6.49659i −0.435044 0.435044i 0.455296 0.890340i \(-0.349533\pi\)
−0.890340 + 0.455296i \(0.849533\pi\)
\(224\) 2.75974 + 2.75974i 0.184393 + 0.184393i
\(225\) 4.98130 + 0.432008i 0.332087 + 0.0288005i
\(226\) 7.85255i 0.522344i
\(227\) −16.6142 −1.10273 −0.551363 0.834265i \(-0.685892\pi\)
−0.551363 + 0.834265i \(0.685892\pi\)
\(228\) 2.84578i 0.188466i
\(229\) 2.86631i 0.189411i −0.995505 0.0947056i \(-0.969809\pi\)
0.995505 0.0947056i \(-0.0301910\pi\)
\(230\) −1.88663 2.05733i −0.124401 0.135656i
\(231\) 1.36784 0.0899974
\(232\) −6.14644 + 6.14644i −0.403534 + 0.403534i
\(233\) 8.37425 8.37425i 0.548615 0.548615i −0.377425 0.926040i \(-0.623190\pi\)
0.926040 + 0.377425i \(0.123190\pi\)
\(234\) 3.27075i 0.213816i
\(235\) −18.2069 0.788024i −1.18769 0.0514050i
\(236\) 10.6205 10.6205i 0.691337 0.691337i
\(237\) 3.49594i 0.227085i
\(238\) −19.5215 19.5215i −1.26539 1.26539i
\(239\) 16.9584 16.9584i 1.09695 1.09695i 0.102185 0.994765i \(-0.467417\pi\)
0.994765 0.102185i \(-0.0325834\pi\)
\(240\) 2.23398 + 0.0966903i 0.144203 + 0.00624133i
\(241\) 9.32818 + 9.32818i 0.600881 + 0.600881i 0.940546 0.339665i \(-0.110314\pi\)
−0.339665 + 0.940546i \(0.610314\pi\)
\(242\) 10.8772i 0.699211i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −1.30384 + 1.30384i −0.0834698 + 0.0834698i
\(245\) −13.5670 + 12.4414i −0.866767 + 0.794849i
\(246\) 3.94446 3.94446i 0.251489 0.251489i
\(247\) −6.58164 6.58164i −0.418780 0.418780i
\(248\) 2.76854 + 2.76854i 0.175802 + 0.175802i
\(249\) 15.0040 0.950840
\(250\) 6.81623 + 8.86223i 0.431096 + 0.560496i
\(251\) −21.5270 + 21.5270i −1.35877 + 1.35877i −0.483333 + 0.875437i \(0.660574\pi\)
−0.875437 + 0.483333i \(0.839426\pi\)
\(252\) 2.75974 + 2.75974i 0.173847 + 0.173847i
\(253\) −0.437515 −0.0275063
\(254\) −14.6420 14.6420i −0.918719 0.918719i
\(255\) −15.8024 0.683957i −0.989587 0.0428310i
\(256\) 1.00000 0.0625000
\(257\) −0.409575 −0.0255486 −0.0127743 0.999918i \(-0.504066\pi\)
−0.0127743 + 0.999918i \(0.504066\pi\)
\(258\) 2.28533 2.28533i 0.142279 0.142279i
\(259\) −3.64895 + 23.4580i −0.226735 + 1.45761i
\(260\) −5.39030 + 4.94305i −0.334292 + 0.306555i
\(261\) −6.14644 + 6.14644i −0.380455 + 0.380455i
\(262\) −3.62929 3.62929i −0.224218 0.224218i
\(263\) 10.0366 10.0366i 0.618882 0.618882i −0.326362 0.945245i \(-0.605823\pi\)
0.945245 + 0.326362i \(0.105823\pi\)
\(264\) 0.247821 0.247821i 0.0152523 0.0152523i
\(265\) −0.472795 + 10.9237i −0.0290435 + 0.671035i
\(266\) −11.1067 −0.680994
\(267\) 4.29357 0.262762
\(268\) 10.6169 + 10.6169i 0.648533 + 0.648533i
\(269\) 19.9758i 1.21794i 0.793192 + 0.608972i \(0.208418\pi\)
−0.793192 + 0.608972i \(0.791582\pi\)
\(270\) 2.23398 + 0.0966903i 0.135955 + 0.00588438i
\(271\) 11.0572 0.671678 0.335839 0.941919i \(-0.390980\pi\)
0.335839 + 0.941919i \(0.390980\pi\)
\(272\) −7.07368 −0.428905
\(273\) −12.7653 −0.772589
\(274\) −12.5315 12.5315i −0.757057 0.757057i
\(275\) 1.74581 + 0.151407i 0.105276 + 0.00913016i
\(276\) −0.882722 0.882722i −0.0531336 0.0531336i
\(277\) 24.4538i 1.46929i −0.678453 0.734644i \(-0.737349\pi\)
0.678453 0.734644i \(-0.262651\pi\)
\(278\) 3.66631i 0.219890i
\(279\) 2.76854 + 2.76854i 0.165748 + 0.165748i
\(280\) −0.377368 + 8.71889i −0.0225521 + 0.521053i
\(281\) −7.23968 7.23968i −0.431883 0.431883i 0.457385 0.889269i \(-0.348786\pi\)
−0.889269 + 0.457385i \(0.848786\pi\)
\(282\) −8.14998 −0.485324
\(283\) 30.2054 1.79552 0.897761 0.440483i \(-0.145193\pi\)
0.897761 + 0.440483i \(0.145193\pi\)
\(284\) −15.8980 −0.943373
\(285\) −4.68993 + 4.30080i −0.277808 + 0.254757i
\(286\) 1.14631i 0.0677825i
\(287\) 15.3946 + 15.3946i 0.908717 + 0.908717i
\(288\) 1.00000 0.0589256
\(289\) 33.0370 1.94335
\(290\) −19.4186 0.840469i −1.14030 0.0493540i
\(291\) −5.61638 + 5.61638i −0.329238 + 0.329238i
\(292\) 0.998067 0.998067i 0.0584075 0.0584075i
\(293\) −0.618270 0.618270i −0.0361197 0.0361197i 0.688816 0.724936i \(-0.258131\pi\)
−0.724936 + 0.688816i \(0.758131\pi\)
\(294\) −5.82110 + 5.82110i −0.339494 + 0.339494i
\(295\) 33.5536 + 1.45226i 1.95357 + 0.0845537i
\(296\) 3.58895 + 4.91116i 0.208603 + 0.285455i
\(297\) 0.247821 0.247821i 0.0143800 0.0143800i
\(298\) 16.9433 0.981499
\(299\) 4.08307 0.236130
\(300\) 3.21684 + 3.82779i 0.185724 + 0.220997i
\(301\) 8.91933 + 8.91933i 0.514101 + 0.514101i
\(302\) 10.7953 0.621201
\(303\) −0.363541 0.363541i −0.0208849 0.0208849i
\(304\) −2.01227 + 2.01227i −0.115412 + 0.115412i
\(305\) −4.11925 0.178288i −0.235867 0.0102087i
\(306\) −7.07368 −0.404376
\(307\) 8.55841 + 8.55841i 0.488454 + 0.488454i 0.907818 0.419364i \(-0.137747\pi\)
−0.419364 + 0.907818i \(0.637747\pi\)
\(308\) 0.967210 + 0.967210i 0.0551119 + 0.0551119i
\(309\) 6.41955 6.41955i 0.365195 0.365195i
\(310\) −0.378572 + 8.74670i −0.0215014 + 0.496779i
\(311\) 7.07966 7.07966i 0.401451 0.401451i −0.477293 0.878744i \(-0.658382\pi\)
0.878744 + 0.477293i \(0.158382\pi\)
\(312\) −2.31277 + 2.31277i −0.130935 + 0.130935i
\(313\) 21.8518i 1.23514i −0.786518 0.617568i \(-0.788118\pi\)
0.786518 0.617568i \(-0.211882\pi\)
\(314\) 6.59408 + 6.59408i 0.372126 + 0.372126i
\(315\) −0.377368 + 8.71889i −0.0212623 + 0.491254i
\(316\) 2.47200 2.47200i 0.139061 0.139061i
\(317\) 19.1074 + 19.1074i 1.07318 + 1.07318i 0.997102 + 0.0760779i \(0.0242398\pi\)
0.0760779 + 0.997102i \(0.475760\pi\)
\(318\) 4.88978i 0.274205i
\(319\) −2.15416 + 2.15416i −0.120610 + 0.120610i
\(320\) 1.51129 + 1.64803i 0.0844837 + 0.0921277i
\(321\) 1.88592i 0.105262i
\(322\) 3.44514 3.44514i 0.191990 0.191990i
\(323\) 14.2342 14.2342i 0.792010 0.792010i
\(324\) 1.00000 0.0555556
\(325\) −16.2926 1.41299i −0.903751 0.0783786i
\(326\) 7.00131i 0.387767i
\(327\) 3.26578i 0.180598i
\(328\) 5.57830 0.308010
\(329\) 31.8082i 1.75364i
\(330\) 0.782946 + 0.0338872i 0.0430998 + 0.00186543i
\(331\) 2.84439 + 2.84439i 0.156342 + 0.156342i 0.780943 0.624602i \(-0.214739\pi\)
−0.624602 + 0.780943i \(0.714739\pi\)
\(332\) 10.6094 + 10.6094i 0.582268 + 0.582268i
\(333\) 3.58895 + 4.91116i 0.196673 + 0.269130i
\(334\) 14.7018i 0.804447i
\(335\) −1.45177 + 33.5423i −0.0793186 + 1.83261i
\(336\) 3.90286i 0.212918i
\(337\) −12.4436 12.4436i −0.677844 0.677844i 0.281668 0.959512i \(-0.409112\pi\)
−0.959512 + 0.281668i \(0.909112\pi\)
\(338\) 2.30219i 0.125222i
\(339\) 5.55259 5.55259i 0.301575 0.301575i
\(340\) −10.6904 11.6576i −0.579768 0.632225i
\(341\) 0.970295 + 0.970295i 0.0525444 + 0.0525444i
\(342\) −2.01227 + 2.01227i −0.108811 + 0.108811i
\(343\) −3.40077 3.40077i −0.183624 0.183624i
\(344\) 3.23195 0.174255
\(345\) 0.120704 2.78880i 0.00649849 0.150144i
\(346\) −3.00005 3.00005i −0.161284 0.161284i
\(347\) 13.9100i 0.746727i 0.927685 + 0.373363i \(0.121796\pi\)
−0.927685 + 0.373363i \(0.878204\pi\)
\(348\) −8.69238 −0.465961
\(349\) 0.414422i 0.0221835i −0.999938 0.0110918i \(-0.996469\pi\)
0.999938 0.0110918i \(-0.00353069\pi\)
\(350\) −14.9393 + 12.5548i −0.798539 + 0.671085i
\(351\) −2.31277 + 2.31277i −0.123447 + 0.123447i
\(352\) 0.350472 0.0186802
\(353\) 29.7855 1.58532 0.792662 0.609661i \(-0.208695\pi\)
0.792662 + 0.609661i \(0.208695\pi\)
\(354\) 15.0197 0.798287
\(355\) −24.0265 26.2004i −1.27519 1.39057i
\(356\) 3.03601 + 3.03601i 0.160908 + 0.160908i
\(357\) 27.6076i 1.46115i
\(358\) −9.62402 + 9.62402i −0.508645 + 0.508645i
\(359\) 8.57788i 0.452723i −0.974043 0.226362i \(-0.927317\pi\)
0.974043 0.226362i \(-0.0726831\pi\)
\(360\) 1.51129 + 1.64803i 0.0796520 + 0.0868588i
\(361\) 10.9015i 0.573765i
\(362\) 14.0878i 0.740436i
\(363\) −7.69132 + 7.69132i −0.403690 + 0.403690i
\(364\) −9.02641 9.02641i −0.473112 0.473112i
\(365\) 3.15321 + 0.136476i 0.165047 + 0.00714350i
\(366\) −1.84391 −0.0963826
\(367\) −9.30759 + 9.30759i −0.485852 + 0.485852i −0.906995 0.421142i \(-0.861629\pi\)
0.421142 + 0.906995i \(0.361629\pi\)
\(368\) 1.24836i 0.0650752i
\(369\) 5.57830 0.290395
\(370\) −2.66980 + 13.3369i −0.138796 + 0.693351i
\(371\) −19.0841 −0.990798
\(372\) 3.91530i 0.202999i
\(373\) 18.3349 18.3349i 0.949345 0.949345i −0.0494321 0.998777i \(-0.515741\pi\)
0.998777 + 0.0494321i \(0.0157411\pi\)
\(374\) −2.47913 −0.128193
\(375\) −1.44674 + 11.0863i −0.0747093 + 0.572496i
\(376\) −5.76291 5.76291i −0.297199 0.297199i
\(377\) 20.1035 20.1035i 1.03538 1.03538i
\(378\) 3.90286i 0.200741i
\(379\) 0.736373i 0.0378249i 0.999821 + 0.0189125i \(0.00602038\pi\)
−0.999821 + 0.0189125i \(0.993980\pi\)
\(380\) −6.35741 0.275159i −0.326128 0.0141154i
\(381\) 20.7069i 1.06085i
\(382\) −2.11691 + 2.11691i −0.108311 + 0.108311i
\(383\) 2.85854i 0.146065i 0.997330 + 0.0730323i \(0.0232676\pi\)
−0.997330 + 0.0730323i \(0.976732\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) −0.132257 + 3.05573i −0.00674044 + 0.155734i
\(386\) 20.7874 1.05805
\(387\) 3.23195 0.164289
\(388\) −7.94277 −0.403233
\(389\) −14.3095 + 14.3095i −0.725519 + 0.725519i −0.969724 0.244205i \(-0.921473\pi\)
0.244205 + 0.969724i \(0.421473\pi\)
\(390\) −7.30678 0.316250i −0.369993 0.0160139i
\(391\) 8.83049i 0.446577i
\(392\) −8.23228 −0.415793
\(393\) 5.13259i 0.258905i
\(394\) −11.8547 11.8547i −0.597233 0.597233i
\(395\) 7.80984 + 0.338023i 0.392956 + 0.0170078i
\(396\) 0.350472 0.0176119
\(397\) 0.498839 + 0.498839i 0.0250360 + 0.0250360i 0.719514 0.694478i \(-0.244365\pi\)
−0.694478 + 0.719514i \(0.744365\pi\)
\(398\) −6.76638 + 6.76638i −0.339168 + 0.339168i
\(399\) −7.85360 7.85360i −0.393172 0.393172i
\(400\) −0.432008 + 4.98130i −0.0216004 + 0.249065i
\(401\) 10.8582 10.8582i 0.542234 0.542234i −0.381949 0.924183i \(-0.624747\pi\)
0.924183 + 0.381949i \(0.124747\pi\)
\(402\) 15.0146i 0.748861i
\(403\) −9.05520 9.05520i −0.451072 0.451072i
\(404\) 0.514124i 0.0255786i
\(405\) 1.51129 + 1.64803i 0.0750966 + 0.0818913i
\(406\) 33.9251i 1.68368i
\(407\) 1.25783 + 1.72122i 0.0623481 + 0.0853179i
\(408\) −5.00185 5.00185i −0.247628 0.247628i
\(409\) −7.92408 7.92408i −0.391820 0.391820i 0.483515 0.875336i \(-0.339360\pi\)
−0.875336 + 0.483515i \(0.839360\pi\)
\(410\) 8.43043 + 9.19321i 0.416349 + 0.454020i
\(411\) 17.7222i 0.874174i
\(412\) 9.07861 0.447271
\(413\) 58.6196i 2.88448i
\(414\) 1.24836i 0.0613535i
\(415\) −1.45074 + 33.5186i −0.0712141 + 1.64536i
\(416\) −3.27075 −0.160362
\(417\) 2.59247 2.59247i 0.126954 0.126954i
\(418\) −0.705244 + 0.705244i −0.0344946 + 0.0344946i
\(419\) 13.1368i 0.641775i 0.947117 + 0.320887i \(0.103981\pi\)
−0.947117 + 0.320887i \(0.896019\pi\)
\(420\) −6.43202 + 5.89834i −0.313851 + 0.287810i
\(421\) 10.6585 10.6585i 0.519461 0.519461i −0.397947 0.917408i \(-0.630277\pi\)
0.917408 + 0.397947i \(0.130277\pi\)
\(422\) 9.92928i 0.483350i
\(423\) −5.76291 5.76291i −0.280202 0.280202i
\(424\) −3.45760 + 3.45760i −0.167916 + 0.167916i
\(425\) 3.05589 35.2362i 0.148232 1.70920i
\(426\) −11.2416 11.2416i −0.544657 0.544657i
\(427\) 7.19651i 0.348263i
\(428\) −1.33354 + 1.33354i −0.0644593 + 0.0644593i
\(429\) −0.810561 + 0.810561i −0.0391343 + 0.0391343i
\(430\) 4.88441 + 5.32635i 0.235547 + 0.256859i
\(431\) −13.6585 + 13.6585i −0.657907 + 0.657907i −0.954884 0.296978i \(-0.904021\pi\)
0.296978 + 0.954884i \(0.404021\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −16.2196 16.2196i −0.779466 0.779466i 0.200274 0.979740i \(-0.435817\pi\)
−0.979740 + 0.200274i \(0.935817\pi\)
\(434\) −15.2809 −0.733505
\(435\) −13.1367 14.3253i −0.629857 0.686846i
\(436\) −2.30925 + 2.30925i −0.110593 + 0.110593i
\(437\) 2.51203 + 2.51203i 0.120167 + 0.120167i
\(438\) 1.41148 0.0674431
\(439\) 4.52525 + 4.52525i 0.215979 + 0.215979i 0.806801 0.590823i \(-0.201197\pi\)
−0.590823 + 0.806801i \(0.701197\pi\)
\(440\) 0.529665 + 0.577588i 0.0252508 + 0.0275354i
\(441\) −8.23228 −0.392013
\(442\) 23.1363 1.10048
\(443\) −17.5292 + 17.5292i −0.832839 + 0.832839i −0.987904 0.155066i \(-0.950441\pi\)
0.155066 + 0.987904i \(0.450441\pi\)
\(444\) −0.934944 + 6.01048i −0.0443705 + 0.285245i
\(445\) −0.415146 + 9.59172i −0.0196798 + 0.454691i
\(446\) 6.49659 6.49659i 0.307623 0.307623i
\(447\) 11.9807 + 11.9807i 0.566669 + 0.566669i
\(448\) −2.75974 + 2.75974i −0.130385 + 0.130385i
\(449\) 24.1689 24.1689i 1.14060 1.14060i 0.152263 0.988340i \(-0.451344\pi\)
0.988340 0.152263i \(-0.0486561\pi\)
\(450\) −0.432008 + 4.98130i −0.0203650 + 0.234821i
\(451\) 1.95504 0.0920592
\(452\) 7.85255 0.369353
\(453\) 7.63344 + 7.63344i 0.358650 + 0.358650i
\(454\) 16.6142i 0.779745i
\(455\) 1.23428 28.5173i 0.0578638 1.33691i
\(456\) −2.84578 −0.133266
\(457\) −15.3091 −0.716131 −0.358065 0.933697i \(-0.616564\pi\)
−0.358065 + 0.933697i \(0.616564\pi\)
\(458\) 2.86631 0.133934
\(459\) −5.00185 5.00185i −0.233466 0.233466i
\(460\) 2.05733 1.88663i 0.0959236 0.0879646i
\(461\) 19.6061 + 19.6061i 0.913145 + 0.913145i 0.996518 0.0833730i \(-0.0265693\pi\)
−0.0833730 + 0.996518i \(0.526569\pi\)
\(462\) 1.36784i 0.0636377i
\(463\) 25.4617i 1.18331i −0.806192 0.591653i \(-0.798475\pi\)
0.806192 0.591653i \(-0.201525\pi\)
\(464\) −6.14644 6.14644i −0.285341 0.285341i
\(465\) −6.45254 + 5.91716i −0.299229 + 0.274402i
\(466\) 8.37425 + 8.37425i 0.387930 + 0.387930i
\(467\) 18.9252 0.875752 0.437876 0.899035i \(-0.355731\pi\)
0.437876 + 0.899035i \(0.355731\pi\)
\(468\) −3.27075 −0.151191
\(469\) −58.5999 −2.70589
\(470\) 0.788024 18.2069i 0.0363488 0.839820i
\(471\) 9.32544i 0.429694i
\(472\) 10.6205 + 10.6205i 0.488849 + 0.488849i
\(473\) 1.13271 0.0520820
\(474\) 3.49594 0.160574
\(475\) −9.15441 10.8930i −0.420033 0.499807i
\(476\) 19.5215 19.5215i 0.894766 0.894766i
\(477\) −3.45760 + 3.45760i −0.158313 + 0.158313i
\(478\) 16.9584 + 16.9584i 0.775661 + 0.775661i
\(479\) 3.00653 3.00653i 0.137372 0.137372i −0.635077 0.772449i \(-0.719032\pi\)
0.772449 + 0.635077i \(0.219032\pi\)
\(480\) −0.0966903 + 2.23398i −0.00441329 + 0.101967i
\(481\) −11.7386 16.0632i −0.535232 0.732418i
\(482\) −9.32818 + 9.32818i −0.424887 + 0.424887i
\(483\) 4.87216 0.221691
\(484\) −10.8772 −0.494417
\(485\) −12.0038 13.0899i −0.545065 0.594383i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) −42.0200 −1.90411 −0.952054 0.305929i \(-0.901033\pi\)
−0.952054 + 0.305929i \(0.901033\pi\)
\(488\) −1.30384 1.30384i −0.0590221 0.0590221i
\(489\) 4.95068 4.95068i 0.223877 0.223877i
\(490\) −12.4414 13.5670i −0.562043 0.612897i
\(491\) 14.2813 0.644507 0.322254 0.946653i \(-0.395560\pi\)
0.322254 + 0.946653i \(0.395560\pi\)
\(492\) 3.94446 + 3.94446i 0.177830 + 0.177830i
\(493\) 43.4780 + 43.4780i 1.95815 + 1.95815i
\(494\) 6.58164 6.58164i 0.296122 0.296122i
\(495\) 0.529665 + 0.577588i 0.0238067 + 0.0259607i
\(496\) −2.76854 + 2.76854i −0.124311 + 0.124311i
\(497\) 43.8743 43.8743i 1.96803 1.96803i
\(498\) 15.0040i 0.672345i
\(499\) −4.58214 4.58214i −0.205125 0.205125i 0.597067 0.802192i \(-0.296333\pi\)
−0.802192 + 0.597067i \(0.796333\pi\)
\(500\) −8.86223 + 6.81623i −0.396331 + 0.304831i
\(501\) 10.3957 10.3957i 0.464447 0.464447i
\(502\) −21.5270 21.5270i −0.960795 0.960795i
\(503\) 4.41445i 0.196831i 0.995145 + 0.0984153i \(0.0313774\pi\)
−0.995145 + 0.0984153i \(0.968623\pi\)
\(504\) −2.75974 + 2.75974i −0.122928 + 0.122928i
\(505\) 0.847293 0.776991i 0.0377040 0.0345756i
\(506\) 0.437515i 0.0194499i
\(507\) −1.62789 + 1.62789i −0.0722972 + 0.0722972i
\(508\) 14.6420 14.6420i 0.649633 0.649633i
\(509\) −23.7000 −1.05048 −0.525242 0.850953i \(-0.676025\pi\)
−0.525242 + 0.850953i \(0.676025\pi\)
\(510\) 0.683957 15.8024i 0.0302861 0.699744i
\(511\) 5.50880i 0.243695i
\(512\) 1.00000i 0.0441942i
\(513\) −2.84578 −0.125644
\(514\) 0.409575i 0.0180656i
\(515\) 13.7204 + 14.9618i 0.604594 + 0.659297i
\(516\) 2.28533 + 2.28533i 0.100606 + 0.100606i
\(517\) −2.01974 2.01974i −0.0888279 0.0888279i
\(518\) −23.4580 3.64895i −1.03069 0.160326i
\(519\) 4.24271i 0.186234i
\(520\) −4.94305 5.39030i −0.216767 0.236380i
\(521\) 22.6223i 0.991100i −0.868579 0.495550i \(-0.834966\pi\)
0.868579 0.495550i \(-0.165034\pi\)
\(522\) −6.14644 6.14644i −0.269023 0.269023i
\(523\) 38.2884i 1.67424i −0.547023 0.837118i \(-0.684239\pi\)
0.547023 0.837118i \(-0.315761\pi\)
\(524\) 3.62929 3.62929i 0.158546 0.158546i
\(525\) −19.4413 1.68606i −0.848488 0.0735858i
\(526\) 10.0366 + 10.0366i 0.437616 + 0.437616i
\(527\) 19.5838 19.5838i 0.853082 0.853082i
\(528\) 0.247821 + 0.247821i 0.0107850 + 0.0107850i
\(529\) 21.4416 0.932244
\(530\) −10.9237 0.472795i −0.474494 0.0205369i
\(531\) 10.6205 + 10.6205i 0.460891 + 0.460891i
\(532\) 11.1067i 0.481535i
\(533\) −18.2452 −0.790289
\(534\) 4.29357i 0.185801i
\(535\) −4.21309 0.182350i −0.182148 0.00788367i
\(536\) −10.6169 + 10.6169i −0.458582 + 0.458582i
\(537\) −13.6104 −0.587333
\(538\) −19.9758 −0.861217
\(539\) −2.88518 −0.124274
\(540\) −0.0966903 + 2.23398i −0.00416089 + 0.0961350i
\(541\) 8.89780 + 8.89780i 0.382546 + 0.382546i 0.872019 0.489472i \(-0.162811\pi\)
−0.489472 + 0.872019i \(0.662811\pi\)
\(542\) 11.0572i 0.474948i
\(543\) −9.96155 + 9.96155i −0.427491 + 0.427491i
\(544\) 7.07368i 0.303282i
\(545\) −7.29567 0.315769i −0.312512 0.0135260i
\(546\) 12.7653i 0.546303i
\(547\) 7.12339i 0.304574i −0.988336 0.152287i \(-0.951336\pi\)
0.988336 0.152287i \(-0.0486638\pi\)
\(548\) 12.5315 12.5315i 0.535320 0.535320i
\(549\) −1.30384 1.30384i −0.0556465 0.0556465i
\(550\) −0.151407 + 1.74581i −0.00645600 + 0.0744414i
\(551\) 24.7366 1.05382
\(552\) 0.882722 0.882722i 0.0375712 0.0375712i
\(553\) 13.6441i 0.580208i
\(554\) 24.4538 1.03894
\(555\) −11.3184 + 7.54276i −0.480440 + 0.320172i
\(556\) 3.66631 0.155486
\(557\) 45.3868i 1.92310i −0.274626 0.961551i \(-0.588554\pi\)
0.274626 0.961551i \(-0.411446\pi\)
\(558\) −2.76854 + 2.76854i −0.117202 + 0.117202i
\(559\) −10.5709 −0.447102
\(560\) −8.71889 0.377368i −0.368440 0.0159467i
\(561\) −1.75301 1.75301i −0.0740121 0.0740121i
\(562\) 7.23968 7.23968i 0.305388 0.305388i
\(563\) 5.35148i 0.225538i 0.993621 + 0.112769i \(0.0359720\pi\)
−0.993621 + 0.112769i \(0.964028\pi\)
\(564\) 8.14998i 0.343176i
\(565\) 11.8675 + 12.9412i 0.499268 + 0.544442i
\(566\) 30.2054i 1.26963i
\(567\) −2.75974 + 2.75974i −0.115898 + 0.115898i
\(568\) 15.8980i 0.667066i
\(569\) 13.2588 + 13.2588i 0.555837 + 0.555837i 0.928119 0.372283i \(-0.121425\pi\)
−0.372283 + 0.928119i \(0.621425\pi\)
\(570\) −4.30080 4.68993i −0.180141 0.196440i
\(571\) −39.9897 −1.67352 −0.836758 0.547574i \(-0.815552\pi\)
−0.836758 + 0.547574i \(0.815552\pi\)
\(572\) −1.14631 −0.0479295
\(573\) −2.99376 −0.125066
\(574\) −15.3946 + 15.3946i −0.642560 + 0.642560i
\(575\) 6.21845 + 0.539300i 0.259327 + 0.0224904i
\(576\) 1.00000i 0.0416667i
\(577\) 2.19671 0.0914503 0.0457251 0.998954i \(-0.485440\pi\)
0.0457251 + 0.998954i \(0.485440\pi\)
\(578\) 33.0370i 1.37416i
\(579\) 14.6989 + 14.6989i 0.610865 + 0.610865i
\(580\) 0.840469 19.4186i 0.0348986 0.806313i
\(581\) −58.5584 −2.42941
\(582\) −5.61638 5.61638i −0.232807 0.232807i
\(583\) −1.21179 + 1.21179i −0.0501873 + 0.0501873i
\(584\) 0.998067 + 0.998067i 0.0413003 + 0.0413003i
\(585\) −4.94305 5.39030i −0.204370 0.222861i
\(586\) 0.618270 0.618270i 0.0255405 0.0255405i
\(587\) 40.3393i 1.66498i −0.554041 0.832490i \(-0.686915\pi\)
0.554041 0.832490i \(-0.313085\pi\)
\(588\) −5.82110 5.82110i −0.240058 0.240058i
\(589\) 11.1421i 0.459102i
\(590\) −1.45226 + 33.5536i −0.0597885 + 1.38138i
\(591\) 16.7651i 0.689625i
\(592\) −4.91116 + 3.58895i −0.201847 + 0.147505i
\(593\) −14.1348 14.1348i −0.580448 0.580448i 0.354579 0.935026i \(-0.384624\pi\)
−0.935026 + 0.354579i \(0.884624\pi\)
\(594\) 0.247821 + 0.247821i 0.0101682 + 0.0101682i
\(595\) 61.6747 + 2.66938i 2.52841 + 0.109434i
\(596\) 16.9433i 0.694025i
\(597\) −9.56911 −0.391638
\(598\) 4.08307i 0.166969i
\(599\) 23.9120i 0.977016i −0.872559 0.488508i \(-0.837541\pi\)
0.872559 0.488508i \(-0.162459\pi\)
\(600\) −3.82779 + 3.21684i −0.156269 + 0.131327i
\(601\) −24.5648 −1.00202 −0.501009 0.865442i \(-0.667038\pi\)
−0.501009 + 0.865442i \(0.667038\pi\)
\(602\) −8.91933 + 8.91933i −0.363525 + 0.363525i
\(603\) −10.6169 + 10.6169i −0.432355 + 0.432355i
\(604\) 10.7953i 0.439255i
\(605\) −16.4386 17.9259i −0.668322 0.728792i
\(606\) 0.363541 0.363541i 0.0147678 0.0147678i
\(607\) 28.5020i 1.15686i 0.815732 + 0.578430i \(0.196334\pi\)
−0.815732 + 0.578430i \(0.803666\pi\)
\(608\) −2.01227 2.01227i −0.0816084 0.0816084i
\(609\) 23.9887 23.9887i 0.972070 0.972070i
\(610\) 0.178288 4.11925i 0.00721867 0.166783i
\(611\) 18.8490 + 18.8490i 0.762550 + 0.762550i
\(612\) 7.07368i 0.285937i
\(613\) −20.5098 + 20.5098i −0.828384 + 0.828384i −0.987293 0.158909i \(-0.949202\pi\)
0.158909 + 0.987293i \(0.449202\pi\)
\(614\) −8.55841 + 8.55841i −0.345389 + 0.345389i
\(615\) −0.539368 + 12.4618i −0.0217494 + 0.502508i
\(616\) −0.967210 + 0.967210i −0.0389700 + 0.0389700i
\(617\) −14.5571 14.5571i −0.586047 0.586047i 0.350511 0.936559i \(-0.386008\pi\)
−0.936559 + 0.350511i \(0.886008\pi\)
\(618\) 6.41955 + 6.41955i 0.258232 + 0.258232i
\(619\) −22.6423 −0.910070 −0.455035 0.890474i \(-0.650373\pi\)
−0.455035 + 0.890474i \(0.650373\pi\)
\(620\) −8.74670 0.378572i −0.351276 0.0152038i
\(621\) 0.882722 0.882722i 0.0354224 0.0354224i
\(622\) 7.07966 + 7.07966i 0.283869 + 0.283869i
\(623\) −16.7572 −0.671362
\(624\) −2.31277 2.31277i −0.0925849 0.0925849i
\(625\) −24.6267 4.30392i −0.985070 0.172157i
\(626\) 21.8518 0.873372
\(627\) −0.997366 −0.0398310
\(628\) −6.59408 + 6.59408i −0.263132 + 0.263132i
\(629\) 34.7400 25.3871i 1.38517 1.01225i
\(630\) −8.71889 0.377368i −0.347369 0.0150347i
\(631\) 23.0961 23.0961i 0.919443 0.919443i −0.0775462 0.996989i \(-0.524709\pi\)
0.996989 + 0.0775462i \(0.0247085\pi\)
\(632\) 2.47200 + 2.47200i 0.0983309 + 0.0983309i
\(633\) 7.02106 7.02106i 0.279062 0.279062i
\(634\) −19.1074 + 19.1074i −0.758853 + 0.758853i
\(635\) 46.2587 + 2.00215i 1.83572 + 0.0794531i
\(636\) −4.88978 −0.193893
\(637\) 26.9257 1.06684
\(638\) −2.15416 2.15416i −0.0852839 0.0852839i
\(639\) 15.8980i 0.628916i
\(640\) −1.64803 + 1.51129i −0.0651441 + 0.0597390i
\(641\) −42.5772 −1.68170 −0.840849 0.541269i \(-0.817944\pi\)
−0.840849 + 0.541269i \(0.817944\pi\)
\(642\) −1.88592 −0.0744312
\(643\) 19.1904 0.756794 0.378397 0.925643i \(-0.376475\pi\)
0.378397 + 0.925643i \(0.376475\pi\)
\(644\) 3.44514 + 3.44514i 0.135757 + 0.135757i
\(645\) −0.312498 + 7.22010i −0.0123046 + 0.284291i
\(646\) 14.2342 + 14.2342i 0.560036 + 0.560036i
\(647\) 28.2302i 1.10984i 0.831903 + 0.554921i \(0.187251\pi\)
−0.831903 + 0.554921i \(0.812749\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 3.72219 + 3.72219i 0.146109 + 0.146109i
\(650\) 1.41299 16.2926i 0.0554220 0.639048i
\(651\) −10.8052 10.8052i −0.423489 0.423489i
\(652\) 7.00131 0.274193
\(653\) 5.24225 0.205145 0.102573 0.994726i \(-0.467293\pi\)
0.102573 + 0.994726i \(0.467293\pi\)
\(654\) −3.26578 −0.127702
\(655\) 11.4661 + 0.496272i 0.448017 + 0.0193910i
\(656\) 5.57830i 0.217796i
\(657\) 0.998067 + 0.998067i 0.0389383 + 0.0389383i
\(658\) 31.8082 1.24001
\(659\) −30.0925 −1.17224 −0.586119 0.810225i \(-0.699345\pi\)
−0.586119 + 0.810225i \(0.699345\pi\)
\(660\) −0.0338872 + 0.782946i −0.00131906 + 0.0304761i
\(661\) −32.5054 + 32.5054i −1.26432 + 1.26432i −0.315335 + 0.948981i \(0.602117\pi\)
−0.948981 + 0.315335i \(0.897883\pi\)
\(662\) −2.84439 + 2.84439i −0.110550 + 0.110550i
\(663\) 16.3598 + 16.3598i 0.635362 + 0.635362i
\(664\) −10.6094 + 10.6094i −0.411726 + 0.411726i
\(665\) 18.3041 16.7854i 0.709804 0.650910i
\(666\) −4.91116 + 3.58895i −0.190303 + 0.139069i
\(667\) −7.67296 + 7.67296i −0.297098 + 0.297098i
\(668\) 14.7018 0.568830
\(669\) 9.18757 0.355212
\(670\) −33.5423 1.45177i −1.29585 0.0560867i
\(671\) −0.456959 0.456959i −0.0176407 0.0176407i
\(672\) −3.90286 −0.150556
\(673\) −9.11977 9.11977i −0.351541 0.351541i 0.509141 0.860683i \(-0.329963\pi\)
−0.860683 + 0.509141i \(0.829963\pi\)
\(674\) 12.4436 12.4436i 0.479308 0.479308i
\(675\) −3.82779 + 3.21684i −0.147332 + 0.123816i
\(676\) −2.30219 −0.0885456
\(677\) 19.8062 + 19.8062i 0.761213 + 0.761213i 0.976542 0.215329i \(-0.0690823\pi\)
−0.215329 + 0.976542i \(0.569082\pi\)
\(678\) 5.55259 + 5.55259i 0.213246 + 0.213246i
\(679\) 21.9199 21.9199i 0.841210 0.841210i
\(680\) 11.6576 10.6904i 0.447050 0.409958i
\(681\) 11.7480 11.7480i 0.450186 0.450186i
\(682\) −0.970295 + 0.970295i −0.0371545 + 0.0371545i
\(683\) 9.00362i 0.344514i −0.985052 0.172257i \(-0.944894\pi\)
0.985052 0.172257i \(-0.0551060\pi\)
\(684\) −2.01227 2.01227i −0.0769411 0.0769411i
\(685\) 39.5911 + 1.71357i 1.51270 + 0.0654721i
\(686\) 3.40077 3.40077i 0.129842 0.129842i
\(687\) 2.02679 + 2.02679i 0.0773268 + 0.0773268i
\(688\) 3.23195i 0.123217i
\(689\) 11.3089 11.3089i 0.430837 0.430837i
\(690\) 2.78880 + 0.120704i 0.106168 + 0.00459513i
\(691\) 8.79710i 0.334657i 0.985901 + 0.167329i \(0.0535141\pi\)
−0.985901 + 0.167329i \(0.946486\pi\)
\(692\) 3.00005 3.00005i 0.114045 0.114045i
\(693\) −0.967210 + 0.967210i −0.0367413 + 0.0367413i
\(694\) −13.9100 −0.528016
\(695\) 5.54085 + 6.04219i 0.210176 + 0.229193i
\(696\) 8.69238i 0.329484i
\(697\) 39.4592i 1.49462i
\(698\) 0.414422 0.0156861
\(699\) 11.8430i 0.447943i
\(700\) −12.5548 14.9393i −0.474529 0.564653i
\(701\) 6.74494 + 6.74494i 0.254753 + 0.254753i 0.822916 0.568163i \(-0.192346\pi\)
−0.568163 + 0.822916i \(0.692346\pi\)
\(702\) −2.31277 2.31277i −0.0872899 0.0872899i
\(703\) 2.66065 17.1045i 0.100348 0.645109i
\(704\) 0.350472i 0.0132089i
\(705\) 13.4314 12.3170i 0.505856 0.463884i
\(706\) 29.7855i 1.12099i
\(707\) 1.41885 + 1.41885i 0.0533612 + 0.0533612i
\(708\) 15.0197i 0.564474i
\(709\) −27.6225 + 27.6225i −1.03739 + 1.03739i −0.0381132 + 0.999273i \(0.512135\pi\)
−0.999273 + 0.0381132i \(0.987865\pi\)
\(710\) 26.2004 24.0265i 0.983284 0.901698i
\(711\) 2.47200 + 2.47200i 0.0927072 + 0.0927072i
\(712\) −3.03601 + 3.03601i −0.113779 + 0.113779i
\(713\) 3.45613 + 3.45613i 0.129433 + 0.129433i
\(714\) 27.6076 1.03319
\(715\) −1.73240 1.88915i −0.0647881 0.0706501i
\(716\) −9.62402 9.62402i −0.359666 0.359666i
\(717\) 23.9829i 0.895656i
\(718\) 8.57788 0.320124
\(719\) 11.0173i 0.410878i 0.978670 + 0.205439i \(0.0658622\pi\)
−0.978670 + 0.205439i \(0.934138\pi\)
\(720\) −1.64803 + 1.51129i −0.0614185 + 0.0563224i
\(721\) −25.0546 + 25.0546i −0.933081 + 0.933081i
\(722\) −10.9015 −0.405713
\(723\) −13.1920 −0.490617
\(724\) −14.0878 −0.523567
\(725\) 33.2726 27.9620i 1.23571 1.03848i
\(726\) −7.69132 7.69132i −0.285452 0.285452i
\(727\) 8.80697i 0.326632i −0.986574 0.163316i \(-0.947781\pi\)
0.986574 0.163316i \(-0.0522191\pi\)
\(728\) 9.02641 9.02641i 0.334541 0.334541i
\(729\) 1.00000i 0.0370370i
\(730\) −0.136476 + 3.15321i −0.00505122 + 0.116706i
\(731\) 22.8618i 0.845574i
\(732\) 1.84391i 0.0681528i
\(733\) −11.9215 + 11.9215i −0.440331 + 0.440331i −0.892123 0.451792i \(-0.850785\pi\)
0.451792 + 0.892123i \(0.350785\pi\)
\(734\) −9.30759 9.30759i −0.343549 0.343549i
\(735\) 0.795982 18.3907i 0.0293602 0.678352i
\(736\) 1.24836 0.0460151
\(737\) −3.72094 + 3.72094i −0.137063 + 0.137063i
\(738\) 5.57830i 0.205340i
\(739\) 1.03649 0.0381277 0.0190639 0.999818i \(-0.493931\pi\)
0.0190639 + 0.999818i \(0.493931\pi\)
\(740\) −13.3369 2.66980i −0.490273 0.0981438i
\(741\) 9.30784 0.341932
\(742\) 19.0841i 0.700600i
\(743\) −16.2854 + 16.2854i −0.597453 + 0.597453i −0.939634 0.342181i \(-0.888834\pi\)
0.342181 + 0.939634i \(0.388834\pi\)
\(744\) −3.91530 −0.143542
\(745\) −27.9231 + 25.6062i −1.02302 + 0.938140i
\(746\) 18.3349 + 18.3349i 0.671289 + 0.671289i
\(747\) −10.6094 + 10.6094i −0.388179 + 0.388179i
\(748\) 2.47913i 0.0906459i
\(749\) 7.36046i 0.268945i
\(750\) −11.0863 1.44674i −0.404816 0.0528274i
\(751\) 44.5447i 1.62546i −0.582641 0.812729i \(-0.697981\pi\)
0.582641 0.812729i \(-0.302019\pi\)
\(752\) 5.76291 5.76291i 0.210152 0.210152i
\(753\) 30.4437i 1.10943i
\(754\) 20.1035 + 20.1035i 0.732126 + 0.732126i
\(755\) −17.7910 + 16.3148i −0.647481 + 0.593758i
\(756\) −3.90286 −0.141945
\(757\) −6.50328 −0.236366 −0.118183 0.992992i \(-0.537707\pi\)
−0.118183 + 0.992992i \(0.537707\pi\)
\(758\) −0.736373 −0.0267463
\(759\) 0.309369 0.309369i 0.0112294 0.0112294i
\(760\) 0.275159 6.35741i 0.00998108 0.230607i
\(761\) 30.3235i 1.09923i −0.835419 0.549613i \(-0.814775\pi\)
0.835419 0.549613i \(-0.185225\pi\)
\(762\) 20.7069 0.750131
\(763\) 12.7459i 0.461431i
\(764\) −2.11691 2.11691i −0.0765871 0.0765871i
\(765\) 11.6576 10.6904i 0.421483 0.386512i
\(766\) −2.85854 −0.103283
\(767\) −34.7371 34.7371i −1.25428 1.25428i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 20.4408 + 20.4408i 0.737113 + 0.737113i 0.972018 0.234906i \(-0.0754781\pi\)
−0.234906 + 0.972018i \(0.575478\pi\)
\(770\) −3.05573 0.132257i −0.110121 0.00476621i
\(771\) 0.289614 0.289614i 0.0104302 0.0104302i
\(772\) 20.7874i 0.748154i
\(773\) −12.8496 12.8496i −0.462167 0.462167i 0.437198 0.899365i \(-0.355971\pi\)
−0.899365 + 0.437198i \(0.855971\pi\)
\(774\) 3.23195i 0.116170i
\(775\) −12.5949 14.9870i −0.452422 0.538347i
\(776\) 7.94277i 0.285129i
\(777\) −14.0071 19.1675i −0.502503 0.687632i
\(778\) −14.3095 14.3095i −0.513019 0.513019i
\(779\) −11.2251 11.2251i −0.402179 0.402179i
\(780\)